Delegation in Strategic Environments and Equilibrium Uniqueness

2026-02-24

AI Summary

This study addresses the challenge of ensuring unique equilibrium predictions in strategic environments where decisions can be delegated to intermediaries—such as platforms or cartels. It models two settings: one where intermediaries lack enforcement power, leading to coarse correlated equilibria (CCE), and another where they possess punitive capabilities, yielding individually rational correlated distributions (IRCP). The work characterizes the game structures that guarantee uniqueness in both solution concepts and uncovers a structural link between CCE and IRCP. Building on this connection, it establishes novel conditions for the uniqueness of Nash and correlated equilibria that do not rely on dominant strategies. The resulting equilibria are shown to be robust to informational perturbations, communication protocols, selection mechanisms, and learning dynamics. The paper provides necessary and sufficient conditions for equilibrium uniqueness, offering a theoretical foundation for collusion-resistant mechanism design and significantly enhancing the stability of equilibrium predictions in complex real-world settings.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

We ask when a normal-form game yields a single equilibrium prediction, even if players can coordinate by delegating play to an intermediary such as a platform or a cartel. Delegation outcomes are modeled via coarse correlated equilibria (CCE) when the intermediary cannot punish deviators, and via the set of individually rational correlated profiles (IRCP) when it can. We characterize games in which the IRCP or the CCE is unique, uncovering a structural link between these solution concepts. Our analysis also provides new conditions for the uniqueness of classical correlated and Nash equilibria that do not rely on the existence of dominant strategies. The resulting equilibria are robust to players' information about the environment, payoff perturbations, pre-play communication, equilibrium selection, and learning dynamics. We apply these results to collusion-proof mechanism design.

Problem

• equilibrium uniqueness
• delegation
• coarse correlated equilibrium
• individually rational correlated profiles
• strategic environments

Innovation

• coarse correlated equilibrium
• individually rational correlated profiles
• equilibrium uniqueness
• strategic delegation
• collusion-proof mechanism design